Almost all oil and gas produced today comes from accumulations in the pore spaces of reservoir rocks—usually sandstones, limestones, or dolomites. The amount of oil and gas contained in a unit volume of the reservoir is the product of its porosity and the hydrocarbon saturation. In addition to porosity and hydrocarbon saturation, the volume of the formation containing hydrocarbon is needed in order to estimate total reserves. Knowledge of the thickness and the area of the reservoir is needed for computation of its volume. To evaluate the producibility of a reservoir, it is necessary to know how easily fluid can flow through the pore system. This property of the formation rock, which depends upon the manner in which the pores are interconnected, is its permeability. Thus the main pertophysical parameters needed to evaluate a reservoir are its porosity, hydrocarbon saturation, thickness, area, and permeability.
Unfortunately, few of these pertophysical parameters can be measured directly. Instead, they must be derived or inferred from the measurement of other physical parameters of the formations. They include, among others, resistivity, the bulk density, hydrogen content (also known as hydrogen index), the natural radioactivity, response to magnetization, the spontaneous potential, etc.
Logging is the process of gathering and recording geological information from deep within the earth. A log (or well log) is a measurement versus depth or time, or both, of one or more physical quantities in or around a well. Wireline logs are taken downhole, transmitted through a wireline to surface and recorded there. Measurements-while-drilling (MWD) and logging-while-drilling (LWD) logs are also taken downhole. They are either transmitted to surface by mud pulses (transmitting pressure pulses in the mud), or else recorded downhole and retrieved later when the instrument is brought to surface. A logging tool carries out measurements from which petrophysical properties of the earth in its vicinity can be derived. This process is often called well log analysis or formation evaluation.
Various logging tools are employed, either separately or in combination, to gather logs of the aforementioned formation parameters. For example, since resistivity of oil and gas is much higher than that of water with dissolved salts, oil soaked rock generally has a higher resistivity than water soaked rock. Thus, a resistivity log can give an indication of what is in the ground. The following paragraphs briefly introduce a few logging tools.
Density logs are primarily used as porosity logs. A radioactive source, applied to the borehole wall, emits medium-energy gamma rays into the formations. These gamma rays may be thought of as high-velocity particles that collide with the electrons in the formation. At each collision a gamma ray loses some, but not all, of its energy to the electron, and then continues with diminished energy. This type of interaction is known as Compton-scattering. The scattered gamma rays reaching the detector, at a fixed distance from the source, are counted as an indication of formation density. See J. S. Wahl, et al., The Dual Spacing Formation Density Log, J. Pet. Tech., December 1964.
The number of Compton-scattering collisions is related directly to the number of electrons in the formation. Consequently, the response of the density tool is determined essentially by the electron density (number of electrons per cubic centimeter) of the formation. Electron density is related to the true bulk density, ρ, which in turn depends on the density of the rock matrix material, the formation porosity, and the density of the fluids filling the pores. A density well log measurement may be expressed in the form shown below in Equation (1);ρ=ρwatνwat+ρoilνoil+ρgasνgas+ρm(1−νwat−νoil−νgas)   (1)where the density, ρ, is the bulk density measured by the well log tool, and ρwat, ρoil, ρgas, and ρm are the average densities of water, oil, gas, and the formation, respectively. Although density logs are quite effective in analyzing the formation porosity, errors may enter the well log analysis due to the presence of shale, and due high fluid pressure.
Another example of a logging tool is a conductivity logging tool. This tool sends a current through the formation and measures the developed voltage. The ratio of the measured current and voltage gives the conductivity of the formation. Conductivity has units of siemens per meter. Most formations logged for potential oil and gas saturation are made up of rocks which, when dry, will not conduct an electric current; i.e., the rock matrix has almost zero conductivity and very high resistivity. An electrical current will flow only through the interstitial water saturating the pore structure of the formation. Conductivity measurements are essential for saturation determinations. Conductivity measurements, along with porosity and water resistivity, are used to obtain values of water and hydrocarbon saturation. The following equation may be used in connection with data obtained from a conductivity tool:CXO=Cmfνwatm   (2)where CXO, Cmf, and νwatm, are the conductivity at a given water saturation conductivity of mud filtrate, and volume of water in the mud formation, respectively. The exponent m is an empirical constant.
Yet another example of a well log measurement is nuclear magnetic resonance (NMR). NMR logs are used for porosity determination, permeability estimation, and fluid characterization. The primary NMR measurement is porosity. The NMR signal amplitude is directly proportional to the amount of hydrogen in the fluids in the formation. Since the fluids fill the pore space, this amplitude constitutes a direct measure of formation porosity, provided that all fluids have the same hydrogen index. In fact, many liquids encountered in oil reservoirs do have comparable hydrogen indices. Gas, condensates, and some light oils, on the other hand, typically have low hydrogen indices, and contribute lower NMR amplitudes than equivalent volumes of water or black oils. Gas zones can often be identified by comparing the NMR log with a density or sonic porosity. An example of the representation of the NMR porosity log measurement is shown in the following equation:MRP=HIwatνwat+HIoilνoil+HIgasνgas   (3)where, HIwat, HIoil, and HIgas are the hydrogen indices of water, oil, and gas, respectively; and νwat, νoil, and νgas are the fluid volumes of water, oil, and gas, respectively.
All the above well log tools and their measurements can be labeled as conventional well log tools and conventional well log measurements, respectively. The following paragraphs briefly describe the Nuclear Magnetic Resonance (NMR) tool.
Modern NMR logging tools use large permanent magnets to create a strong static magnetic polarizing field inside the formation. The hydrogen nuclei of water and hydrocarbons are electrically charged spinning protons that create weak magnetic fields—like tiny bar magnets. When the strong external magnetic field from the logging tool passes through a formation containing fluids, these spinning protons align themselves like compass needles along the magnetic field. This process, called polarization, increases exponentially with a time constant, T1, as long as the external magnetic field is applied. A magnetic pulse from the antenna rotates, or s the aligned protons into a plane perpendicular, or transverse, to the polarization field. These tipped protons immediately start to wobble or precess around the direction of the strong logging-tool magnetic field.
The precession frequency, called the Larmor frequency, is proportional to the strength of the external magnetic field. The precessing protons create an oscillating magnetic field, which generate a weak radio signal at this frequency. The total signal amplitude from all the precessing hydrogen nuclei (typically a few microvolts) is a measure of the total hydrogen content, which is a measure of porosity of the formation.
The rate at which the proton precession decays is called the transverse relaxation time, T2, and is the second key NMR measurement because it is related to the pore-size distribution. T2 measures the rate at which the spinning protons lose their alignment within the transverse plane. It depends on three factors: the intrinsic bulk-relaxation rate in the fluid; the surface-relaxation rate, which is an environmental effect; and relaxation from diffusion in a field gradient which is a combination of environmental and tool effects. There is no diffusion contribution to T1.
The spinning protons will quickly lose their relative phase alignment within the transverse plane because of variations in the static magnetic field. This process is called the free induction decay (FID), and the Carr-Purcell-Meiboom-Gill (CPMG) pulse-echo sequence is used to compensate for the rapid free-induction decay caused by reversible transverse dephasing effects.
The three components of the transverse relaxation time play a significant role in the use of the T2 distribution for well logging applications. For example, the intrinsic bulk relaxation time is caused principally by the magnetic interactions between neighboring spinning protons in the fluid molecules. These are often called spin-spin interactions. Molecular motion in water and light oil is rapid, so the relaxation in large pores is inefficient with correspondingly long decay-time constants. However, as liquids become more viscous, the molecular motion is slower. Then the spin-spin interactions become much more efficient. Thus, tar and viscous oils can be identified because they have shorter T2 decay times than light oil or water.
Fluids near or in contact with grain surfaces relax at a much higher rate than the bulk fluid relaxation rate. Because of complex atomic level electromagnetic field interactions at the grain surface there is a high probability that the spinning proton in the fluid will relax when it encounters a grain surface. For the surface relaxation process to dominate the decay time, the spinning protons in the fluid must make multiple encounters with the surface, caused by Brownian motion, across small pores in the formation. They repeatedly collide with the surface until a relaxation event occurs. The resulting T2 distribution leads to a natural measure of the pore-size distribution.
The approach described above comes from early generation NMR logging tools which typically measure simple echo trains that only reflect T2 distributions. The latest generation NMR tools acquire more complex datasets that contain information not only about T2 distributions but also about T1 distributions (longitudinal relaxation time) and molecular diffusion rates, D. These properties—in particular molecular diffusion rates—are highly dependent on the fluid types, as explained below.
Relaxation from diffusion is a technique frequently used to differentiate oil from gas. See R. Akkurt et al., NMR Logging of Natural Gas Reservoirs, The Log Analyst, no. 6 November-December 1996. Between spin-flipping pulses, some protons will drift—due to their Brownian motion—from one region to another of different field strength, which changes their precession rate. As a result, they will not receive the correct phase adjustment for their previous polarization environment. This leads to an increase in the observed transverse dephasing relaxation rate. Gas has relatively high mobility compared with oil and water, and therefore, the spinning protons in gas have a much larger diffusion effect.
The preceding paragraphs described various logging techniques that can be used for formation evaluation. Once the data are collected they are usually input to a data processing unit that performs log analysis. An important objective of all log analysis is to determine the mineral and fluid volumes that constitute the earth formation as a function of depth. This is achieved by analyzing a plurality of log measurements (multi-tool analysis). In general, the physical properties measured by the tools are not the fluid or mineral volumes themselves. Log analysis is then performed by first expressing each logging tool response in terms of the volumes, and then computing the set of volumes that provide the overall best agreement between the computed tool responses and the actual measured values.
For each tool, the physical properties submitted to the log analysis are themselves derived by previous processing of raw data such as count rates (gamma ray log), voltage amplitudes, frequencies, and signal phase differences. For NMR tools, the pre-processing stage involves calibration (in terms of NMR volume fractions) of echo amplitudes and the mathematical inversion of echo amplitude decays to provide T2 (transverse relaxation time) distributions. The quantity eventually submitted to the multi-tool analysis is the NMR porosity, which is the sum of the amplitudes in the T2 distribution. In some cases a NMR bound fluid volume, computed as the sum of T2 distribution components falling below a specified T2 cutoff value, is also given as an input to the analysis. The NMR porosity and bound fluid volumes are related to the formation fluid volumes by the respective fluid hydrogen indices.
However, current multi-tool log analysis techniques take no account of diffusion effects on the transverse relaxation time. Instead, NMR fluid analysis is performed independently and results are then compared with the results of conventional multi-tool analysis. Although this approach is useful in environments where conventional methods may be inaccurate (e.g., low resistivity pay), in many other cases it does not take full advantage of all the available data.
Mathematical inversion of NMR data takes NMR properties (namely relaxation times T1 and/or T2 and Diffusion D) and relates these properties to specific fluids. Two types of NMR inversion have been proposed for diffusion-based NMR logs. The first type is a model-based approach, one example of which is the Magnetic Resonance Fluid (MRF) characterization method as described in U.S. Pat. No. 6,229,308 issued to Freedman et al. This method involves making multiple NMR measurements with different parameters and simultaneously analyzing all the data in an inversion. The MRF method invokes the Constituent Viscosity Model (CVM), which relates relaxation time and diffusion rates to phenomenological constituent viscosities whose geometric mean is identical to the macroscopic fluid viscosity. In addition to fluid volumes, the method provides estimates of the oil viscosity. The MRF technique represents the most comprehensive and accurate method currently available for NMR fluid characterization in well logging. Unlike previous methods, the MRF method is applicable to any suite of NMR measurements and is not limited to CPMG sequences and is commonly applied to diffusion editing (DE) measurements.
The second type of inversion is independent of any fluid model. Instead, the 3D-NMR method, as described in Chanh Cao Minh et al., Planning and Interpreting NMR Fluid-Characterization Logs, SPE paper 84478, presented at the SPE Annual Technical Conference and Exhibition, 5-8 Oct. 2003, Denver, Colo.; and Nicholas J. Heaton et al, Saturation and Viscosity from Multidimensional Nuclear Magnetic Resonance Logging, SPE paper 90564, presented at the SPE Annual Technical Conference and Exhibition, 26-29 Sep. 2004, Houston, Tex., provides a graphical representation of the NMR responses in the form of cross-plots (often referred to as maps) of NMR properties such as D vs. T2 or D vs. T1. By inspecting these D-T1 and D-T2 maps it is often possible to identify different fluids and assign NMR responses to them based on the location of the corresponding peaks in the maps. Fluid volumes can be computed either by direct integration of the peak amplitudes if the peaks are well-resolved or by applying deconvolution methods (equivalent to MRF analysis) if they are not.
An alternative approach to NMR fluid-typing involves the comparison of different measurements acquired at different depths of investigation (See U.S. Pat. No. 6,703,832 issued to Heaton et al.). This method exploits the variation in fluid saturations at different depths of investigation caused by invading mud filtrate. In general, deeper measurements are more likely to sense native fluids while shallower measurements sense a greater proportion of filtrate. Because the filtrate NMR response is generally known, differences in NMR response between the two sets of measurements provide an indication of the fluid type at the deeper depth of investigation.
All of the techniques described above rely on measuring NMR properties, namely relaxation times and diffusion rates and relating these properties to specific fluids. The principal attractions of the NMR methods are (a) that they can function in environments where conventional resistivity-based saturation analysis is unsuitable or inaccurate (eg. low contrast or low resistivity pay), and (b) that they can also provide information on oil viscosity. The extended range of viscosity estimate derived from combined NMR data has significant potential in heavy oil reservoirs.